To solve the equation, we first need to simplify the expression on the left side:

X^2 - 3x - 1 - 2x^2*x - 5/2 = 1.5
Combine like terms and simplify the expression:

-X^3 - 3x - 1 - 2x^3 - 5/2 = 1.5
-3x - 1 - 2x^3 - 5/2 = 1.5
-3x - 1 - 2x^3 - 2.5 = 1.5
-3x - 1 - 2x^3 - 2.5 = 1.5
-3x - 2x^3 - 3.5 = 1.5
-3x - 2x^3 = 1.5 + 3.5
-3x - 2x^3 = 5
-2x^3 - 3x = 5
Rearranging the equation:
-2x^3 - 3x - 5 = 0

This is a cubic equation that can be solved by factoring, using the rational root theorem, or other methods.